Estimated That Of Non-negative Matrix Perron Roots Of The Upper And Lower Bounds

For matrices of high orders, it is very difficult to obtain their exact eigenvalues, so it is particularly important to local the eigenvalues by rows, columns or minors of matrices. In my paper, by using the theory of Frobenius, we obtain the better transformation by selecting transformation of matrix to get different rows and columns, and get better estimation for upper and low bounds of Perron root .In chapter 2, we mainly discusses the general methods to local the eigenvalues of matrices, and introduce achievements about upper and low bounds of Perron root by matrix experts A.Braue, O.Taussky, R.S.Verga, and A.Ostrowski etc. Many techniques can be introduced the estimation of eigenvalues of deferent matrices, for instant, theory of plane and the relation of trace and eigenvalues of matrix. We also introduce arithmetic to calculate Perron root.In chapter 3, we mainly discuss the low bound of Perron root of irreducible nonnegative matrix and obtain a better low bound of Perron root of irreducible nonnegative matrix by using similar transformation of matrix and the theory of Frobenius.In chapter 4, we mainly obtain a better upper bound of Perron root of irreducible nonnegative matrix by using deferent transformation of matrix in chapter 3 and the theory of Frobenius.